Resilient State Recovery using Prior Measurement Support Information

Resilient state recovery of cyber-physical systems has attracted much research attention due to the unique challenges posed by the tight coupling between communication, computation, and the underlying physics of such systems. By modeling attacks as additive adversary signals to a sparse subset of measurements, this resilient recovery problem can be formulated as an error correction problem. To achieve exact state recovery, most existing results require less than $50\%$ of the measurement nodes to be compromised, which limits the resiliency of the estimators. In this paper, we show that observer resiliency can be further improved by incorporating data-driven prior information. We provide an analytical bridge between the precision of prior information and the resiliency of the estimator. By quantifying the relationship between the estimation error of the weighted $\ell_1$ observer and the precision of the support prior. This quantified relationship provides guidance for the estimator's weight design to achieve optimal resiliency. Several numerical simulations and an application case study are presented to validate the theoretical claims.